The Generalized Boltzmann Physical Kinetics: History, the Last Achievements and Perspectives

Dr. Boris V. Alexeev

Moscow Fine Chemical Technology Institute

March 21, 1997

Abstract

In 1872 Boltzmann derived his well known equation within the context of the kinetic theory of gases and now, more than one hundred years later, the Boltzmann equation (BE) has an extremely wide range of applications.

From the theoretical point of view, BE is a powerful tool (and very often the only tool) for the investigations of many transport processes. It is the reason why from the beginning the basic principles of the Boltzmann kinetic theory (BKT) were the topic of consideration in many papers and discussions.

In spite of the obvious achievements of BKT, many problems (like strict theory of turbulence) in modern physics remain without solutions.

In the last decade considerable efforts have been done in creation of the generalized Boltzmann kinetic theory (GBKT) on the basement of the generalized Boltzmann equation (BGE). It is well known that BE is valid for the hydrodynamic scale and also for scales related to the mean free path between collisions. Generalization of the classical BKT proposed by Alexeev takes into account the third possible scale, i.e. alteration of the distribution function on the collision time order. It is extremely important that obtained additional terms in BE are of the order of Knudsen number and cannot be omitted even by small Knudsen numbers, because these additional terms contain Kn-like small coefficients at senior derivatives.

Many applications of the new kinetic theory have been considered in the last years, including: the generalized hydrodynamic equations (GHE) and their applications in the theory of turbulent gas flows; propagation of the ultrasonic waves in gases; shock waves structure investigation using HGE; physics of weakly ionized gases, including the influence of electromagnetic fields on the transport properties; propagation of main ideas of GBKT into the theory of liquids.

The review of this research and the main results will be presented, including comparison with experiment data.